From a university student to a chief academician

Chapter 14 Finding Proof Ideas
MIT, the library!

Gao Fei looked at Ye Fei's new paper.

"Condition (H4) is equivalent to b(0)N={1, 2, 3, .}, and it will be seen that condition (H4) is the only necessary condition for the existence of a solution to a power series of the form..."

"Power series solution, power series solution..." Gao Fei muttered to himself, his eyes became brighter and brighter.

"Yes!" He clenched his fists excitedly suddenly, and said, "Just solve it like this."

The people around were interrupted by him to read, and looked at him irritably.

Gao Fei found himself speaking loudly and disturbing others from reading, so he shrank his neck.

He said excitedly in his heart: "I have found a solution, so let's solve it like this."

"Ye Fei is really my lucky star. The two months are about to expire, and I have found a solution. Ye Feifei is doomed."

"I don't believe he can find a solution from Ye Fei's thesis."

Gao Fei is full of blind confidence in himself, because he has never lost in his studies since he was a child.

Long-term victories bring great confidence.

Ten days later!
Ye Fei glanced at the system, and the progress of the task of exploring the singular cardinality problem reached 95%.

When he published the paper on the basis of singular cardinality, the task progress reached 40%.

When the first solution is published, the task progress reaches 50%.

The second solution is 60%, the third solution is 70%, and the fourth solution is 90%
After another week of study, the task progress reached 95%
"There's only 5% left." Ye Fei exhaled lightly, and said distressedly: "But how to solve it next?"

The road to scientific research is more difficult as you go up.

After three days of hard work, the 5% Ye Fei did not make any progress.

This is like a moat, blocking his research on singular bases.

"Two months are up, ask Gao Feixiang if he found it."

Ye Fei sent a message to Gao Fei through Stack Exchange: "Gao Feixiang, have you thought of the proof of the singular cardinal number?"

Gao Fei made a fool of himself and asked, "What about you?"

"I haven't thought of it yet."

Gao Fei was very excited when he saw Ye Fei's answer. Sure enough, as he expected, he did not find the proof of the singular cardinality.

Gao Fei replied: "I have found an idea from a class of function spaces."

"Isn't it a proof method?" Ye Fei asked.

"What are you thinking?" Gao Fei curled his lips and continued to reply: "The problem that the singular base number has not been solved for 149 years, you still want to solve it in two months!"

After Ye Fei saw it, he shook his head regretfully. He had his own ideas, but what he wanted now was a way to prove it.

Ye Fei said: "Then tell me about your thinking."

"OK!" Gao Fei replied: "My idea is found from the Tribel-Ledrokin space in a class of function spaces, the weighted Maury-type Bissault space and the Tribel-Ledrokin space. Fourier's multiplier theorem."

"The boundedness of a class of pseudo-differential operators with non-regular signs can be obtained."

"And then get the real Euclidean space and Schwartz space..."

Ye Fei looked at Gao Fei's explanation, when Gao Fei said that the low frequency part is considered by the previous lemma, and only needs to focus on the high frequency part.

He suddenly felt like a small universe exploded in his mind, and a flash of light flashed in his mind.

"Yes, that's the case, from low frequency to high frequency, and then use space to find the differential operator."

Ye Fei connected the five papers on singular bases written during this period with the ideas just thought of, forming a complete singular base proof method.

The first paper was the basis of singular cardinal numbers and four singular cardinal number solutions, all of which led him to the door of singular cardinal numbers.

But now there is still a key missing, and now he has found this key, which is to use space to find out the differential operator.

"So, my method and his method prove that the singular cardinality is correct."

"My method is the way, sending me to the gate of the singular base, and his method is to make a key to open this door."

"So the two of us can't say who wins and who loses?"

Ye Fei laughed again in his heart and said, "But without my way, I wouldn't be able to get to this door!"

"Of course, I can't open this door without his key."

"Also, his current thinking can't make a key. With his help, I used my own method to make this key."

Ye Fei glanced at the system, the task progress was 100%.

He said in surprise: "Sure enough, my thinking is right."

Gao Fei said: "I'm done talking, how about it, now you are convinced!"

Ye Fei said: "I am convinced, of course I am convinced."

He complained in his heart: "Looking at this person's ability, he must have been in the world of mathematics for a long time. He should be over 30 years old, and how he speaks is similar to a 20-year-old girl."

Gao Fei said: "Then use my method to explore the singular base!"

"Okay, no problem." Ye Fei said: "But you explore first, I have to wait for half a month, some things are very busy recently, we will continue after half a month."

He was going to write a paper on the proof of singular cardinal numbers, but he couldn't tell others about it.

After it is written, it will be posted on Arxiv, and it will be useless for others to know.

Is this plagiarism?
Not counting, there are many papers on Arxiv.

If there are a small number of other people's papers in one's own paper, it is counted as a citation at most.

Besides, when papers are sent to journals, journals also need to review the repetition rate.

If the repetition rate is high, the first trial will not pass.

Gao Fei pouted, a little unhappy, and agreed to explore the singular base together, why is this person like this!
But he also knows that people always have three urgencies, maybe the other party is really busy, and he can't stop him.

He replied: "Okay, then you hurry up."

"OK!" Ye Fei replied.

End the conversation with Goofy and exit Stack Exchange.

Gao Fei looked at Ye Feifei's head turned into black and white, and suddenly said: "By the way, I haven't asked who he is yet, forget it, next time!"

He remembered the task his mentor had given him.

Ye Fei quickly opened Word, recorded the ideas that came to mind, and then began to plan the outline.

This paper, is to prove the singular cardinality.

It is very important, so he needs to plan well.

[Algorithm Proving Singular Cardinality of Non-regular Graph Isomorphism]

On September 9st, the university starts!
Many new and former students, undergraduates, postgraduates and doctoral students, begin admission.

When they entered the school gate, they all saw a banner above the school gate.

[Congratulations to Ye Fei, a graduate student of the School of Mathematics of our school, for entering the SCI Zone [-] with five papers]

Many people were blinded and envious when they saw this banner.

After seeing it, many parents pointed and told their children to follow this man named Ye Fei as an example.

Even if some parents are not educated, they don't know what SCI is.

But your children always know, ask them what SCI is.

After some science popularization by their own children, they know what it means to enter SCI.

When many university professors saw this banner, they were envious and jealous.

Why doesn't their academy have a genius like Ye Fei!

Before they even came to school, they heard that there was a genius in the School of Mathematics.

In just one vacation, five papers were entered into the first area of ​​SCI.

They are all about set theory, and one of them is very important, which is the basis for proving singular cardinality.

It's like a holiday has passed, and the whole world has changed a lot.

Zhuang Nan came with a group of people. With his back to the door, he said excitedly, "Let me tell you, my roommate Ye Fei is amazing. He published five papers, all of which entered SCI Zone [-]."

Zhuang Nan is worthy of being a young expert in intelligence. Ever since he knew that Ye Fei's paper had entered SCI Zone [-], he has been paying attention to Ye Fei's paper.

He read all the papers published by Ye Fei on Arxiv, and he also went to Stack Exchange to support Ye Fei.

Of course, he accidentally leaked some information about Ye Fei.

For example, Ye Fei's age, Ye Fei is his roommate, Ye Fei has a good relationship with him...

A person next to him pointed to the banner on the gate and said, "Zhuang Nan, we all know about Ye Fei, look."

Zhuang Nan turned around to look, dumbfounded, and said: "The school is too licking!"

Zhou Lindao: "If you can complete five SCI area [-] papers in a short period of time, the school will do the same."

Zhuang Nan said discouragedly: "Forget it, I can't do it."

On this day, Ye Fei became famous at Zhonghu University.

Freshmen, old students, lecturers, professors, deans, principals.

We all know that Ye Fei, School of Mathematics, Zhonghu University, has five papers entered into the first area of ​​SCI.

This is a dazzling record. It is very difficult for ordinary people to enter the first division of SCI with one paper, let alone five.

(End of this chapter)